• Jun 26 2012

    WITS Node Seminar: Dr Rytis Paškauskas

    The National Institute for Theoretical Physics, and the Centre for Theoretical Physics, School of Physics, would like to invite to its coming talk in the theory seminar series, entitled:

    "Equilibration in the Curie-Weiss anisotropic quantum Heisenberg model"

    to be presented by Dr. Rytis Paškauskas (NITheP/Stellenbosch)

    Abstract: Equilibration in a quantum spin model with mean-field interactions is explored, following the principle that if sufficiently many ``generic,'' noncommuting observables approach their equilibrium values, then the system as a whole equilibrates. The questions pondered in this talk are: What is the rate of relaxation of a certain class of observables? Are there initial states, perhaps atypical, that have odd dynamical patterns?

    In the framework of the quantum Bogoliubov-Born-Green-Kirkwood-Yvon
    (BBGKY) hierarchy, an unconventional representation that is different from the usual cluster expansion is introduced, which casts the hierarchy into the form of a second-order recursion. This coefficient representation allows to classify all symmetries of the equations of motion for arbitrary coupling parameters of the model: It is found that there are either 2, 4, or O(N) symmetry subspaces, and the coefficient BBGKY hierarchy decouples into the corresponding number of Hermitian Liouville operators on each subspace. The complexity of these Liouvillians does not permit an analytic solution in general. A novel approach of solving the problem is proposed, whereby instead of being numerically diagonalized, the Liouville operator is first tridiagonalized by using the stabilized Lanczos algorithm. As a result, the Green's operator is expressed in terms of a certain orthogonal polynomial sequence with numerically computed coefficients of recursion.
    By Fourier transforming their orthogonality weight function, evolution of selected observables may be determined. This approach provides a framework within which more questions about subtleties of this model can be answered in some cases analytically, and in all other cases by a mixture of analytic insights and an efficient computational algorithm that can reach the thermodynamic limit. This methodology does not make the matrix product or other simplifying assumptions about the structure of the density matrix. Nevertheless it appears to be uniquely positioned to provide detailed answers to the aforementioned questions.

    Date: Tuesday, 26th June 2012
    Venue: Frank Nabarro Lecture Theatre P216
    Time: 13.20 - 14.10

    For more information please contact:

    Alan S. Cornell

    School of Physics
    University of the Witwatersrand
    Private Bag 3
    Wits 2050
    South Africa